Cognitive Radio Simultaneous Spectrum Access/ One-shot Game Modelling Ligia C. Cremene*,***, D. Dumitrescu**,***, Réka Nagy**, Noemi Gasko** *
**
Technical University of Cluj-Napoca, Department of Communications, Adaptive Systems Laboratory, Romania Babeş-Bolyai University, Department of Computer Science, Centre for the Study of Complexity, Cluj-Napoca, Romania *** Romanian Institute of Science and Technology, Cluj-Napoca, Romania
[email protected], {ddumitr, reka, gasko}@cs.ubbcluj.ro
Abstract— The aim of this paper is to asses simultaneous spectrum access situations that may occur in Cognitive Radio (CR) environments. The approach is that of one-shot, noncooperative games describing CR interactions. Open spectrum access scenarios are modelled based on continuous and discrete reformulations of the Cournot game theoretical model. CR interaction situations are described by Nash and Pareto equilibria. Also, the heterogeneity of players is captured by the new concept of joint Nash-Pareto equilibrium, allowing CRs to be biased toward different types of equilibrium. Numerical simulations reveal equilibrium situations that may be reached in simultaneous access scenarios of two and three users. Keywords - open spectrum access, cognitive radio environments, spectrum-aware communications, non-cooperative one-shot games.
I.
INTRODUCTION
Cognitive radio (CR) technology is seen as the key enabler for next generation communication networks, which will be spectrum-aware, dynamic spectrum access networks [1], [2], [3]. Cognitive radios (CRs) hold the promise for an efficient use of the radio resources and are seen as the solution to the current low usage of the radio spectrum [2], [4], [5]. In a CR environment users strategically compete for spectrum resources in dynamic scenarios. In this paper the problem of simultaneous, open spectrum access is addressed from a game theoretical perspective. Game Theory (GT) provides a fertile framework and the computational tools for CR interaction analysis. By devising GT simulations, insight may be gained on unanticipated situations that may arise in spectrum access. Clearly CR interactions are strategic interactions [8]: the utility of one CR agent/player depends on the actions of all the other CRs in the area. The proposed approach relies on the following assumptions: (i) CRs have perfect channel sensing and RF reconfiguration capabilities [2], [6], [7], (ii) CRs are myopic, self-regarding players, (iii) repeated interaction among the same CRs is not likely to occur on a regular basis [9], and (iv) CRs do not know in advance what actions the other CRs will choose. These are reasons to consider one-shot, non-cooperative games for the open spectrum access analysis.
An oligopoly competition game model – Cournot – is reformulated in terms of spectrum access. Continuous and discrete instances of the game are analyzed. Nash and Pareto equilibria are revisited for the discrete instance of the game. Heterogeneity of players is captured by joint Nash-Pareto equilibria, allowing CRs to be biased toward different types of equilibrium. The paper is structured as follows: Section II provides some basic insights on game-equilibria detection. The reformulation of Cournot game theoretic model for simultaneous, open spectrum access is described in Section III. Section IV discusses simulation results obtained for continuous and discrete instances of the game. Conclusions are presented in Section V. II.
GAME EQUILIBRIA IN BRIEF
A strategic-form game model is defined by its three major components: a finite set of players, a set of actions, and a payoff/utility function which measures the outcome for each player, determined by the actions of all players [8], [10]. A game may be defined as a system G = ((N, Si, ui), i = 1,…, n) where: (i) N represents the set of n players, N = {1,…, n}. (ii) for each player i є N, Si represents the set of actions Si = {si1, si2, …, sim}; S = S1 × S 2 × ...S n is the set of all possible game situations; (iii) for each player i є N, ui :S → R represents the payoff function. A strategy profile is a vector s = ( s1 ,..., sn ), where
si ∈ S i is a strategy (or action) of player i. By ( si , s −* i ) we denote the strategy profile obtained from s* by replacing the strategy of player i with si, i.e.
( si , s −*i ) = ( s1* , s2* ,..., si*−1 , si , si*+1 ,..., sn* ). A strategy profile in which each player’s strategy is a best response to the strategies of the other players is a Nash equilibrium (NE) [8], [11]. Informally, a strategy profile is a Nash equilibrium if no player can improve her payoff by unilateral deviation. Considering two strategy profiles x and y from S, the strategy profile x is said to Pareto dominate the strategy profile
y (and we write x
